AOI Logic Implementation
Digital Electronics
© 2014 Project Lead The Way, Inc.
AOI Logic Implementation
This presentation will demonstrate how to…
• Design an AOI logic circuit from a
Sum-Of-Products (SOP) logic expression.
• Design an AOI logic circuit from a
Product-Of-Sums (POS) logic expression.
OUT  A B  B C
Logic Expression
EQUALS
AOI Logic Circuit
2
Designing (AOI)
Sum of Product (SOP) Logic Circuits
Design Steps
• Implement each Minterm in the logic expression with an
AND gate with the same number of inputs as there are
variables in the Minterm. (i.e., AB = 2 input gate, ABC = 3
input gate, ABCD = 4 input gate, etc.)
• OR together the outputs of the AND gates to produce the
logic expression.
• If necessary, gates can be cascaded to create gates with
more inputs.
3
Example #1:
Sum of Product (SOP) Logic Circuits
Design an AOI Logic Circuit for the SOP logic
expression shown below.
F1  A B C D  B C D  A B
4
Example #1:
Sum of Product (SOP) Logic Circuits
Design an AOI Logic Circuit for the SOP logic
expression shown below.
F1  A B C D  B C D  A B
Solution
F1
5
Example #2:
Sum of Product (SOP) Logic Circuits
In this class, we only have access to 2-input OR
gates, 2-input AND gates, and 3-input AND gates.
Limiting your design to these gates, redesign the AOI
Logic Circuit for the SOP expression in the previous
example.
6
Example #2:
Sum of Product (SOP) Logic Circuits
In this class, we only have access to 2-input OR
gates, 2-input AND gates, and 3-input AND gates.
Limiting your design to these gates, redesign the AOI
Logic Circuit for the SOP expression in the previous
example.
Solution
F1
7
Designing (AOI)
Product of Sum (POS) Logic Circuits
Design Steps
• Implement each Maxterm in the logic expression with an
OR gate with the same number of inputs as there are
variables in the Maxterm. (i.e., A+B = 2 input gate,
A+B+C = 3 input gate, A+B+C+D = 4 input gate, etc.)
• AND together the outputs of the OR gates to produce the
logic expression.
• If necessary, gates can be cascaded to create gates with
more inputs.
8
Example #3:
Product of Sum (POS) Logic Circuits
Example
Design an AOI Logic Circuit for the POS logic
expression shown below.



F2  W  X  Y  Z W  X  Y W  Z

9
Example #3:
Product of Sum (POS) Logic Circuits
Design an AOI Logic Circuit for the POS logic
expression shown below.
Solution



F2  W  X  Y  Z W  X  Y W  Z

F2
10
Example #4:
Product of Sum (POS) Logic Circuits
Limiting your design to only 2-input OR gates, 2-input
AND gates, and 3-input AND gates redesign the AOI
Logic Circuit for the POS logic expression in the
previous example.
11
Example #4:
Product of Sum (POS) Logic Circuits
Limiting your design to only 2-input OR gates, 2-input
AND gates, and 3-input AND gates redesign the AOI
Logic Circuit for the POS logic expression in the
previous example.
Solution
F2
12